A cascadic geometric filtering approach to subdivision
A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be ...
Self-intersection avoidance and integral properties of generalized cylinders
A generalized cylinder is an object bounded by a surface generated by moving a 2D contour curve along a 3D spine curve, possibly scaling the contour along the spine, and two end planes. Several important properties of such objects are presented. In ...
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction
We study the relationship of transformations between Legendre and Bernstein basis. Using the relationship, we present a simple and efficient method for optimal multiple degree reductions of Bézier curves with respect to the L2-norm.
Efficient topology determination of implicitly defined algebraic plane curves
This paper is devoted to present a new algorithm computing in a very efficient way the topology of a real algebraic plane curve defined implicitly. This algorithm proceeds in a seminumerical way by performing a symbolic preprocessing which allows later ...
